DELTA-SHOCK WAVES AS LIMITS OF VANISHING VISCOSITY FOR HYPERBOLIC SYSTEMS OF CONSERVATION-LAWS

[摘要] For simple models of hyperbolic systems of conservation laws, we study a new type of nonlinear hyperbolic wave, a delta-shock wave, which is a Dirac delta function supported on a shock. We prove that delta-shock waves are w*-limits in L1 of solutions to some reasonable viscous perturbations as the viscosity vanishes. Further, we solve the multiplication problem of a delta function with a discontinuous function to show that delta-shock waves satisfy the equations in the sense of distributions. Under suitable generalized Rankine-Hugoniot and entropy conditions, we establish the existence and uniqueness of solutions involving delta-shock waves for the Riemann problems. The existence of solutions to the Cauchy problem is also investigated. (C) 1994 Academic Press, Inc.

[发布日期] 1994-08-01